Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method

Table 7

Nondimensional transverse natural frequencies for axially FG tapered beam; boundary condition: C-C.

		0		0.2		0.4		0.6		0.8
		0	SFPM	20.4721	56.5492	20.4152	56.4716	20.2883	56.2981	20.0186	55.9206	19.3845	54.9713
Reference [3]	20.4721		56.5482	20.4151	56.4706	20.2883	56.2971	20.0186	55.9195	19.3844	54.9699
0.2	SFPM	18.2170	50.4796	18.1996	50.4560	18.1286	50.3593	17.9436	50.1011	17.4565	49.3718
	Reference [3]	18.2170	50.4792	18.1995	50.4556	18.1286	50.3589	17.9436	50.1006	17.4564	49.3711
0.4	SFPM	15.8282	44.0246	15.8498	44.0553	15.8350	44.0371	15.7367	43.9027	15.4025	43.4066
	Reference [3]	15.8281	44.0236	15.8497	44.0542	15.8349	44.0359	15.7366	43.9013	15.4021	43.4043
0.6	SFPM	13.2294	36.9654	13.2896	37.0509	13.3319	37.1137	13.3238	37.1105	13.1529	36.8680
	Reference [3]	13.2291	36.9636	13.2894	37.0490	13.3316	37.1116	13.3234	37.1079	13.1521	36.8635
0.8	SFPM	10.2236	28.7498	10.3231	28.8919	10.4257	29.0416	10.5170	29.1851	10.5343	29.2419
	Reference [3]	10.2217	28.7406	10.3211	28.8822	10.4234	29.0311	10.5143	29.1728	10.5301	29.2239